Friday, April 6, 2012

JCCDQBHWHCB019 Combinatorics : Circular Permutations

Suggested Approach and Solution:-

     Draw a diagram.  Let’s assume that the special woman (W*) is at the 12 o’clock reference position.  [If not, we can always rotate our heads or rotate the table so that she is.] 


Together with the two lucky(?) men M1 and M2, they form one entity.  There are 3C2 x 2!
= 3P2 = 6 ways to choose and arrange these two men to sit besides this special woman.  The other 4 persons can arrange themselves relative to the reference entity in 4! = 24 ways (this is same as (5 – 1)! or 5! / 5).  Hence the number of ways = 6 x 24 = 144.

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